Channel estimation for an OFDM communication system with inactive subbands

ABSTRACT

For channel estimation in a spectrally shaped wireless communication system, an initial frequency response estimate is obtained for a first set of P uniformly spaced subbands (1) based on pilot symbols received on a second set of subbands used for pilot transmission and (2) using extrapolation and/or interpolation, where P is a power of two. A channel impulse response estimate is obtained by performing a P-point IFFT on the initial frequency response estimate. A final frequency response estimate for N total subbands is derived by (1) setting low quality taps for the channel impulse response estimate to zero, (2) zero-padding the channel impulse response estimate to length N, and (3) performing an N-point FFT on the zero-padded channel impulse response estimate. The channel frequency/impulse response estimate may be filtered to obtain a higher quality channel estimate.

BACKGROUND

I. Field

The present invention relates generally to data communication, and morespecifically to techniques for performing channel estimation in anorthogonal frequency division multiplexing (OFDM) communication system.

II. Background

OFDM is a multi-carrier modulation technique that effectively partitionsthe overall system bandwidth into multiple (N) orthogonal subbands.These subbands are also referred to as tones, subcarriers, bins, andfrequency channels. With OFDM, each subband is associated with arespective subcarrier that may be modulated with data.

In a wireless communication system, a radio frequency (RF) modulatedsignal may travel via a number of signal paths from a transmitter to areceiver. If the signal paths have different delays, then the receivedsignal at the receiver would include multiple instances of thetransmitted signal with different gains and delays. This time dispersionin the wireless channel causes frequency selective fading, which ischaracterized by a frequency response that varies across the systembandwidth. For an OFDM system, the N subbands may thus experiencedifferent effective channels and may consequently be associated withdifferent complex channel gains.

An accurate estimate of the wireless channel between the transmitter andthe receiver is normally needed in order to effectively receive data onthe available subbands. Channel estimation is typically performed bysending a pilot from the transmitter and measuring the pilot at thereceiver. Since the pilot is made up of modulation symbols that areknown a priori by the receiver, the channel response can be estimated asthe ratio of the received pilot symbol over the transmitted pilot symbolfor each subband used for pilot transmission.

Pilot transmission represents overhead in the OFDM system. Thus, it isdesirable to minimize pilot transmission to the extent possible. Thiscan be achieved by sending pilot symbols on a subset of the N totalsubbands and using these pilot symbols to derive channel estimates forall subbands of interest. As described below, the computation to derivethe channel estimates can be great for certain systems such as, forexample, (1) a spectrally shaped system that does not transmitdata/pilot near the band edges and (2) a system that cannot transmitdata/pilot on certain subbands (e.g., zero or DC subband). There istherefore a need in the art for techniques to efficiently estimate thechannel response for these systems.

SUMMARY

Techniques to efficiently derive a frequency response estimate for awireless channel in an OFDM system with inactive subbands are describedherein. These techniques may be used for an OFDM system that transmitspilot on subbands that are not uniformly distributed across the N totalsubbands. An example of such a system is a spectrally shaped OFDM systemin which only M subbands, which are centered among the N total subbands,are used for data/pilot transmission and the remaining N-M subbands atthe two band edges are not used and served as guard subbands. Theinactive subbands may thus be the guard subbands, DC subband, and so on.

For the channel estimation, an initial frequency response estimate isobtained for a first set of P uniformly spaced subbands based on, forexample, pilot symbols received on a second set of subbands used forpilot transmission, where P is an integer that is a power of two. Thefirst set includes at least one subband not included in the second set(e.g., pilot subbands among the guard subbands). Moreover, the subbandsin the first set are uniformly spaced apart by N/P subbands.Extrapolation and/or interpolation may be used, as necessary, to obtainthe initial frequency response estimate.

A time-domain channel impulse response estimate for the wireless channelis then derived based on the initial frequency response estimate, forexample, by performing a P-point inverse fast Fourier transform (IFFT).A final frequency response estimate for the N total subbands is thenderived based on the channel impulse response estimate. This may beachieved, for example, by (1) setting low quality taps in the channelimpulse response estimate to zero and retaining the remaining taps, (2)zero-padding the channel impulse response estimate to length N, and (3)performing an N-point fast Fourier transform (FFT) on the zero-paddedchannel impulse response estimate to obtain the final frequency responseestimate. The channel impulse response estimates or frequency responseestimates for multiple OFDM symbols may be filtered to obtain a higherquality channel estimate for the wireless channel.

Various aspects and embodiments of the invention are described infurther detail below.

BRIEF DESCRIPTION OF THE DRAWINGS

The features, nature, and advantages of the present invention willbecome more apparent from the detailed description set forth below whentaken in conjunction with the drawings in which like referencecharacters identify correspondingly throughout and wherein:

FIG. 1 shows an exemplary subband structure for an OFDM system;

FIG. 2 shows a pilot transmission scheme that may be used to obtain afrequency response estimate of a wireless channel;

FIG. 3 shows a uniform pilot transmission scheme that can simplify thecomputation for a least square channel impulse response estimate;

FIG. 4 shows a uniform pilot transmission scheme for a spectrally shapedOFDM system;

FIGS. 5 and 6 show two processes for obtaining the final frequencyresponse estimate for the wireless channel in a spectrally shaped OFDMsystem; and

FIG. 7 shows an access point and a terminal in the OFDM system.

DETAILED DESCRIPTION

The word “exemplary” is used herein to mean “serving as an example,instance, or illustration.” Any embodiment or design described herein as“exemplary” is not necessarily to be construed as preferred oradvantageous over other embodiments or designs.

FIG. 1 shows an exemplary subband structure 100 that may be used for anOFDM system. The OFDM system has an overall system bandwidth of BW MHz,which is partitioned into N orthogonal subbands using OFDM. Each subbandhas a bandwidth of BW/N MHz. In a spectrally shaped OFDM system, only Mof the N total subbands are used for data/pilot transmission, where M<N.The remaining N-M subbands are not used for data/pilot transmission andserve as guard subbands to allow the OFDM system to meet spectral maskrequirements. The M usable subbands include subbands F through F+M−1 andare typically centered among the N total subbands.

The N subbands of the OFDM system may experience different channelconditions (e.g., different fading and multipath effects) and may beassociated with different complex channel gains. An accurate estimate ofthe channel response is normally needed to process (e.g., demodulate anddecode) data at a receiver.

The wireless channel in the OFDM system may be characterized by either atime-domain channel impulse response h_(N×1) or a correspondingfrequency-domain channel frequency response H_(N×1). As used herein, andwhich is consistent with conventional terminology, a “channel impulseresponse” is a time-domain response of the channel, and a “channelfrequency response” is a frequency-domain response of the channel. Thechannel frequency response H_(N×1) is the discrete Fourier transform(DFT) of the channel impulse response h_(N×1). This relationship may beexpressed in matrix form, as follows:H _(N×1) =W _(N×N) h _(N×1),   Eq. (1)where h_(N×1) is an N×1 vector for the impulse response of the wirelesschannel between a transmitter and a receiver in the OFDM system;

-   -   H_(N×1) is an N×1 vector for the frequency response of the        wireless channel; and    -   W_(N×N) is an N×N DFT matrix used to perform the DFT on h_(N×1)        to obtain H_(N×1).

The DFT matrix W_(N×N) is defined such that the (n,m)-th entry w_(n,m)is given as: $\begin{matrix}{{w_{n,m} = {\mathbb{e}}^{{- {j2\pi}}\frac{{({n - 1})}{({m - 1})}}{N}}},{{{for}\quad n} = {{\left\{ {1\ldots\quad N} \right\}\quad{and}\quad m} = \left\{ {1\ldots\quad N} \right\}}},} & {{Eq}\quad(2)}\end{matrix}$where n is a row index and m is a column index.

The impulse response of the wireless channel can be characterized by Ltaps, where L is typically much less than the number of total subbands(i.e., L<N). That is, if an impulse is applied to the wireless channelby the transmitter, then L time-domain samples (at the sample rate of BWMHz) would be sufficient to characterize the response of the wirelesschannel based on this impulse stimulus. The number of taps (L) for thechannel impulse response is dependent on the delay spread of the system,which is the time difference between the earliest and latest arrivingsignal instances of sufficient energy at the receiver. A longer delayspread corresponds to a larger value for L, and vice versa. The vectorh_(N×1) includes one non-zero entry for each tap of the channel impulseresponse. For a delay spread of L, the first L entries of the vectorh_(N×1) may contain non-zero values and the N-L remaining entries areall zeros.

Because only L taps are needed for the channel impulse response, thechannel frequency response H_(N×1) lies in a subspace of dimension L(instead of N). The frequency response of the wireless channel may thusbe fully characterized based on channel gain estimates for as few as Lappropriately selected subbands, instead of all N subbands. Even ifchannel gain estimates for more than L subbands are available, animproved estimate of the frequency response of the wireless channel maybe obtained by suppressing the noise components outside this subspace.

FIG. 2 shows a pilot transmission scheme 200 that may be used to obtaina frequency response estimate for the wireless channel in the OFDMsystem. A pilot symbol is transmitted on each of P pilot subbands, wherein general L≦P≦M. The pilot subbands are distributed among the M usablesubbands and have indices of s₁ through s_(p). Typically, the number ofpilot subbands is much less than the number of usable subbands (i.e.,P<M ). The remaining M-P usable subbands may be used for transmission ofuser-specific data, overhead data, and so on.

The model for the OFDM system may be expressed as:r _(N×1) =H _(N×1) ∘x _(N×1) +n _(N×1),   Eq. (3)where x_(N×1) is an N×1 vector with N “transmit” symbols sent by thetransmitter on the N subbands, with zeros being sent on the unusedsubbands;

-   -   r_(N×1) is an N×1 vector with N “received” symbols obtained by        the receiver for the N subbands;    -   n_(N×1) is an N×1 noise vector for the N subbands; and    -   “∘” denotes the Hadmard product, which is an element-wise        product, where the i-th element of r_(N×1) is the product of the        i-th elements of x_(N×1) and H_(N×1).

The noise n_(N×1) is assumed to be additive white Gaussian noise (AWGN)with zero mean and a variance of σ².

An initial estimate of the frequency response of the wireless channel,${\hat{\underset{\_}{H}}}_{P \times 1}^{init},$may be obtained as follows: $\begin{matrix}{{{\hat{\underset{\_}{H}}}_{P \times 1}^{init} = {{{\underset{\_}{r}}_{P \times 1}^{p}/{\underset{\_}{x}}_{P \times 1}^{p}} = {{\underset{\_}{H}}_{P \times 1}^{p} + {{\underset{\_}{n}}_{P \times 1}^{p}/{\underset{\_}{x}}_{P \times 1}^{p}}}}},} & {{Eq}\quad(4)}\end{matrix}$where x_(P×1) ^(p) is a P×1 vector with P pilot symbols sent on the Ppilot subbands;

-   -   r_(P×1) ^(p) is a P×1 vector with P received pilot symbols for        the P pilot subbands;    -   H_(P×1) ^(p) is a P×1 vector for the actual frequency response        of the P pilot subbands;    -   Ĥ_(P×1) ^(init) is a P×1 vector for the initial frequency        response estimate;    -   n_(P×1) ^(p) is a P×1 noise vector for the P pilot subbands; and    -   r_(P×1) ^(p)/x_(P×1) ^(p)=[{circumflex over (P)}(s₁)/P(s₁)        {circumflex over (P)}(s₂)/P(s₂) . . . {circumflex over        (P)}(s_(p))/P(s_(p))]^(T), where {circumflex over (P)}(s_(i))        and P(s_(i)) are respectively the received and transmitted pilot        symbols for pilot subband s_(i).        The P×1 vectors x_(P×1) ^(p), r_(P×1) ^(p), and n_(P×1) ^(p)        include only P entries of the N×1 vectors x_(N×1), r_(N×1) and        n_(N×1), respectively, corresponding to the P pilot subbands. As        shown in equation (4), the receiver can obtain the initial        frequency response estimate        ${\hat{\underset{\_}{H}}}_{P \times 1}^{init}$        based on P element-wise ratios of the received pilot symbols to        the transmitted pilot symbols for the P pilot subbands, i.e.,        ${{\hat{\underset{\_}{H}}}_{P \times 1}^{init} = \left\lbrack {{\hat{H}\left( s_{1} \right)}\quad{\hat{H}\left( s_{2} \right)}\ldots\quad{\hat{H}\left( s_{p} \right)}} \right\rbrack^{T}},$        where Ĥ(s_(i))={circumflex over (P)}(s_(i))/P(s_(i)) is the        channel gain estimate for subband s_(i). The vector        ${\hat{\underset{\_}{H}}}_{P \times 1}^{init}$        is indicative of the frequency response of the wireless channel        for the P pilot subbands.

A frequency response estimate for the N total subbands may be obtainedbased on the initial frequency response estimate${\hat{\underset{\_}{H}}}_{P \times 1}^{init}$using various techniques. For a direct least-squares estimationtechnique, a least square estimate of the impulse response of thewireless channel is first obtained based on the following optimization:$\begin{matrix}{{{\underset{\_}{\hat{h}}}_{L \times 1}^{ls} = {\min\limits_{{\underset{\_}{h}}_{L \times 1}}{{{\hat{\underset{\_}{H}}}_{P \times 1}^{init} - {{\underset{\_}{W}}_{P \times L}{\underset{\_}{h}}_{L \times 1}}}}^{2}}},} & {{Eq}\quad(5)}\end{matrix}$where h_(L×1) is an L×1 vector for a hypothesized impulse response ofthe wireless channel;

-   -   W_(P×L) is a P×L sub-matrix of W_(N×N; and)    -   ĥ_(L×1) ^(ls) is an L×1 vector for the least square channel        impulse response estimate.

The matrix W_(P×L) contains P rows of the matrix W_(N×N) correspondingto the P pilot subbands. Each row of W_(P×L) contains L elements, whichare the first L elements of the corresponding row of W_(N×N). Theoptimization in equation (5) is over all possible channel impulseresponses h_(L×1). The least square channel impulse response estimateĥ_(L×1) ^(ls) is equal to the hypothesized channel impulse responseh_(L×1) that results in minimum mean square error between the initialfrequency response estimate${\hat{\underset{\_}{H}}}_{P \times 1}^{init}$and the frequency response corresponding to h_(L×1), which is given byW_(P×L)h_(L×1).

The solution to the optimization problem posed in equation (5) may beexpressed as:ĥ _(L×1) ^(ls)=(W _(P×L) ^(H) W _(P×L))⁻¹ W _(P×L) ^(H) Ĥ _(P×1)^(init).   Eq. (6)

The frequency response estimate for the wireless channel may then bederived from the least square channel impulse response estimate, asfollows:Ĥ _(N×1) ^(ls) =W _(N×L) ĥ _(L×1) ^(ls),   Eq. (7)where W_(N×L) is an N×L matrix with the first L columns of W_(N×N); and

-   -   Ĥ_(N×1) ^(ls) is an N×1 vector for the frequency response        estimate for all N subbands.

The vector Ĥ_(N×1) ^(ls) can be computed in several manners. Forexample, the vector ĥ_(L×1) ^(ls) can be computed first as shown inequation (6) and then used to compute the vector Ĥ_(N×1) ^(ls) as shownin equation (7). For equation (6), (W_(P×L) ^(H)W_(P×L))⁻¹W_(P×L) ^(H)is an L×P matrix that can be pre-computed. The impulse response estimateĥ_(L×1) ^(ls) can then be obtained with L·P complex operations (ormultiplications). For equation (7), the frequency response estimateĤ_(N×1) ^(ls) can be more efficiently computed by (1) extending the L×1vector ĥ_(L×1) ^(ls) (with zero padding) to obtain an N×1 vector ĥ_(N×1)^(ls) and (2) performing an N-point FFT on ĥ_(N×1) ^(ls), which requires0.5 N·log N complex operations. The frequency response estimate Ĥ_(N×1)^(ls) can thus be obtained with a total of (L·P+0.5 N·log N) complexoperations for both equations (6) and (7).

Alternatively, the vector Ĥ_(N×1) ^(ls) can be computed directly fromthe vector Ĥ_(P×1) ^(init) by combining equations (6) and (7), asfollows: $\begin{matrix}{{{\hat{\underset{\_}{H}}}_{N \times 1}^{ls} = {{{\underset{\_}{W}}_{N \times L}\left( {{\underset{\_}{W}}_{P \times L}^{H}{\underset{\_}{W}}_{P \times L}} \right)}^{- 1}{\underset{\_}{W}}_{P \times L}^{H}{\hat{\underset{\_}{H}}}_{P \times 1}^{init}}},} & {{Eq}\quad(8)}\end{matrix}$where W_(N×L)(W_(P×L) ^(H)W_(P×L))⁻¹W_(P×L) ^(H) is an N×P matrix thatcan be pre-computed. The frequency response estimate Ĥ_(N×1) ^(ls) canthen be obtained with a total of N·P complex operations.

For the two computation methods described above, the minimum number ofcomplex operations needed to obtain Ĥ_(N×1) ^(ls) for one OFDM symbol isN_(op)=min{(L·P+0.5 N·log N), N·P}. If pilot symbols are transmitted ineach OFDM symbol, then the rate of computation is N_(op)/T_(sym) millionoperations per second (Mops), which is N_(op)·BW/N Mops, where T_(sym)is the duration of one OFDM symbol and is equal to N/BW μsec with nocyclic prefix (described below). The number of complex operations,N_(op), can be very high for an OFDM system with a large number ofsubbands. As an example, for an OFDM system with an overall bandwidth ofBW=6 MHz, N=4096 total subbands, P=512 pilot subbands, and L=512 taps,420 Mops are needed to compute Ĥ_(N×1) ^(ls) using equations (6) and(7). Since equation (6) requires 384 Mops and equation (7) requires 36Mops, the computation for the least square channel impulse responseestimate in equation (6) is significantly more burdensome than thecomputation for the N-point FFT in equation (7).

Pilot transmission scheme 200 in FIG. 2 does not impose a constraint onthe locations of the pilot subbands. The matrix W_(P×L) contains P rowsof the matrix W_(N×N) corresponding to the P pilot subbands. Thisresults in the need for P complex operations for each of the L entriesof the vector ĥ_(L×1) ^(ls).

FIG. 3 shows a uniform pilot transmission scheme 300 that can simplifythe computation for a least square channel impulse response estimateĥ_(P×1) ^(ls). For scheme 300, the P pilot subbands are uniformlydistributed across the N total subbands such that consecutive pilotsubbands are spaced apart by N/P subbands. Furthermore, the number oftaps is assumed to be equal to the number of pilot subbands (i.e., L=P). In this case, W_(P×P) is a P×P DFT matrix, W_(P×P) ^(H)W_(P×P)=Iwhere I is the identity matrix, and equation (6) can be simplified as:ĥ _(P×1) ^(ls) =W _(P×P) ^(H) Ĥ _(P×1) ^(init).   Eq. (9)Equation (9) indicates that the channel impulse response estimateĥ_(P×1) ^(ls) can be obtained by performing a P-point IFFT on theinitial frequency response estimate${\hat{\underset{\_}{H}}}_{P \times 1}^{init}.$The vector ĥ_(P×1) ^(ls) can be zero-padded to length N. The zero-paddedvector ĥ_(N×1) ^(ls) can then be transformed with an N-point FFT toobtain the vector Ĥ_(N×1) ^(ls), as follows:Ĥ _(N×1) ^(ls) =W _(N×N) ĥ _(N×1) ^(ls).   Eq. (10)An S×1 vector Ĥ_(S×1) ^(ls) for the frequency response estimate for Ssubbands of interest may also be obtained based on the vector ĥ_(P×1)^(ls), where in general N≧S≧P. If S is a power of two, then an S-pointFFT can perform to obtain Ĥ_(S×1) ^(ls).

With pilot transmission scheme 300, the number of complex operationsrequired to obtain Ĥ_(N×1) ^(ls) for one OFDM symbol isN_(op)=0.5·(P·log P+N·log N) and the rate of computation is0.5·BW·(P·log P+N·log N)/N Mops. For the exemplary OFDM system describedabove, Ĥ_(N×1) ^(ls) can be computed with 39.38 Mops using pilottransmission scheme 300, which is much less than the 420 Mops needed forpilot transmission scheme 200.

The reduced-complexity least square channel impulse response estimationdescribed above in equations (9) and (10) relies on two key assumptions:

-   -   1. The P pilot subbands are periodic across the N total        subbands, and    -   2. The number of taps is equal to the number of pilot subbands        (i.e., L=P).        These two assumptions impose important restrictions/limitations        in a practical OFDM system. First, for some OFDM systems, it may        not be possible to transmit pilot symbols on P subbands        uniformly distributed across the N total subbands. For example,        in a spectrally shaped OFDM system, no symbols are transmitted        on the guard subbands in order to meet spectral mask        requirements. As another example, an OFDM system may not permit        pilot/data transmission on certain subbands (e.g., zero or DC        subband). As yet another example, pilot may not be available for        some subbands due to receiver filter implementation and/or other        reasons. For these systems, strict periodicity of the P pilot        subbands across the entire N total subbands is typically not        possible. Second, the assumption of L=P (which is less serious        than the first assumption) can degrade the quality of the final        channel frequency response estimate Ĥ_(N×1) ^(ls). It can be        shown that the quality of the channel estimate can degrade by as        much as 3 dB from an optimal channel estimate if (1) L is        assumed to be equal to P, (2) the pilot symbol energy is the        same as the data symbol energy, and (3) time-domain filtering is        not performed on ĥ_(P×1) ^(ls) or Ĥ_(N×1) ^(ls) to capture        additional energy. This amount of degradation in the channel        estimate quality may not be acceptable for some systems.

Various techniques may be used to overcome the two restrictionsdescribed above. First, extrapolation and/or interpolation may be used,as necessary, to obtain channel gain estimates for P uniformly spacedsubbands based on the received pilot symbols. This allows the channelimpulse response estimate ĥ_(P×1) ^(ls) to be derived with a P-pointIFFT. Second, tap selection may be performed on the P elements ofĥ_(P×1) ^(ls) to obtain a higher quality channel estimate.Extrapolation/interpolation and tap selection are described in detailbelow.

FIG. 4 shows a uniform pilot transmission scheme 400 for a spectrallyshaped OFDM system. For scheme 400, the P pilot subbands are uniformlydistributed across the N total subbands such that consecutive pilotsubbands are spaced apart by N/P subbands, similar to scheme 300.However, pilot symbols are transmitted only on pilot subbands that areamong the M usable subbands (or simply, the “active pilot subbands”). Nopilot symbols are transmitted on pilot subbands that are among the N-Mguard subbands (or simply, the “inactive pilot subbands”). The receiverthus obtains pilot symbols for the active pilot subbands and no pilotsymbols for the inactive pilot subbands.

FIG. 5 shows a process 500 for obtaining the frequency response estimateĤ_(N×1) ^(ls) for the wireless channel in the spectrally shaped OFDMsystem. An initial frequency response estimate for a first set of Puniformly spaced subbands is obtained based on, for example, pilotsymbols received on a second set of subbands used for pilot transmission(block 512). The first set includes at least one subband not included inthe second set (e.g., pilot subbands among the guard subbands). Animpulse response estimate for the wireless channel is next derived basedon the initial frequency response estimate (block 514). Channel impulseresponse estimates for multiple OFDM symbols may be filtered to obtain ahigher quality channel estimate (block 516). A final frequency responseestimate for the wireless channel is then derived based on the (filteredor unfiltered) channel impulse response estimate (block 518). Filteringmay also be performed on the initial or final frequency responseestimate (instead of the channel impulse response estimate) to obtainhigher quality channel estimate.

FIG. 6 shows a specific process 600 for obtaining the frequency responseestimate Ĥ_(N×1) ^(ls) in the spectrally shaped OFDM system. Initially,received pilot symbols are obtained for P_(act) active pilot subbandswith pilot transmission (block 610). Channel gain estimates ĥ(s_(i)) forthe P_(act) active pilot subbands are then derived based on the receivedpilot symbols (block 612). The output of block 612 is a P_(act)×1 vector${\hat{\underset{\_}{H}}}_{P_{act} \times 1}^{init}$for the initial frequency response estimate for the P_(act) active pilotsubbands. Extrapolation and/or interpolation are performed as necessaryto obtain channel gain estimates for P_(ext) subbands without pilottransmission, as described below (block 614). The output of block 614 isa P_(ext)×1 vector ${\hat{\underset{\_}{H}}}_{P \times 1}^{init}$for the initial frequency response estimate for the P_(ext) subbandswithout pilot transmission. The P×1 vector${\hat{\underset{\_}{H}}}_{P \times 1}^{init}$for the initial frequency response estimate for P uniformly spacedsubbands is then formed based on the channel gain estimates from thevectors${{\hat{\underset{\_}{H}}}_{P_{act} \times 1}^{init}\quad{and}\quad{\hat{\underset{\_}{H}}}_{P_{ext} \times 1}^{init}},$e.g.,${\hat{\underset{\_}{H}}}_{P \times 1}^{init} = \left\lbrack {{\hat{\underset{\_}{H}}}_{P_{act} \times 1}^{init}\quad{\hat{\underset{\_}{H}}}_{P_{ext} \times 1}^{init}} \right\rbrack^{T}$(block 616). The channel gain estimate for each of the P subbands may bederived based on either a received pilot symbol orextrapolation/interpolation.

A P-point IFFT is then performed on the vector${\hat{\underset{\_}{H}}}_{P \times 1}^{init}$to obtain the P×1 vector ĥ_(P×1) ^(ls) for the least square channelimpulse response estimate, as shown in equation (9) (block 618).Time-domain filtering may be performed on the channel impulse responseestimates ĥ_(P×1) ^(ls) for multiple OFDM symbols to obtain a higherquality channel estimate (block 620). The time-domain filtering may beomitted or may be performed on frequency response estimates instead ofimpulse response estimates. The (filtered or unfiltered) vector ĥ_(P×1)^(ls) includes P entries for L taps, where L is typically less than P.The vector ĥ_(P×1) ^(ls) is then processed to select “good” taps anddiscard or zero out remaining taps, as described below (block 622). Zeropadding is also performed to obtain the N×1 vector ĥ_(N×1) ^(ls) for thechannel impulse response estimate (block 624). An N-point FFT is thenperformed on the vector ĥ_(N×1) ^(ls) to obtain the vector Ĥ_(N×1) ^(ls)for the final frequency response estimate for the N total subbands(block 626).Extrapolation/Interpolation

For block 614 in FIG. 6, extrapolation can be used to obtain channelgain estimates for inactive pilot subbands that are located among theguard subbands. For a function y=f(x), where a set of y values isavailable for a set of x values within a known range, extrapolation canbe used to estimate a y value for an x value outside of the known range.For channel estimation, x corresponds to pilot subband and y correspondsto channel gain estimate. Extrapolation can be performed in variousmanners.

In one extrapolation scheme, the channel gain estimate for each inactivepilot subband is set equal to the channel gain estimate for the nearestactive pilot subband, as follows: $\begin{matrix}{{\hat{H}\left( s_{i} \right)} = \left\{ {\begin{matrix}{\hat{H}\left( s_{b} \right)} & {{{for}\quad s_{i}} < s_{b}} \\{\hat{H}\left( s_{e} \right)} & {{{for}\quad s_{i}} > s_{e}}\end{matrix},} \right.} & {{Eq}\quad(11)}\end{matrix}$where Ĥ(s_(i)) is the channel gain estimate for subband s_(i), s_(b) isthe first active pilot subband, and s_(e) is the last active pilotsubband, as shown in FIG. 4.

In another extrapolation scheme, the channel gain estimate for eachinactive pilot subband is obtained based on a weighted sum of thechannel gain estimates for the active pilot subbands. If the number oftaps L is less than or equal to the number of active pilot subbands(i.e., L≦P_(act)), then (in the absence of noise) the wireless channelcan be completely characterized by the channel gain estimates for theactive pilot subbands. For the extrapolation, each inactive pilotsubband is associated with a respective set of extrapolationcoefficients, one coefficient for each active pilot subband, where eachcoefficient may be a zero or non-zero value. Theextrapolation/interpolation for the inactive pilot subbands may beexpressed in matrix form, as follows: $\begin{matrix}{\quad{{{\hat{\underset{\_}{H}}}_{P_{ext} \times 1}^{init} = {{\underset{\_}{C}}_{P_{ext} \times P_{act}}\quad{\hat{\underset{\_}{H}}}_{P_{act} \times 1}^{init}}},}} & {{Eq}\quad(12)}\end{matrix}$where C_(P) _(ext) _(×P) _(act) is a P_(ext)×P_(act) matrix ofextrapolation coefficients.

The number of complex operations required for extrapolation in equation(12) is P_(ext)·P_(act). The number of inactive pilot subbands is${P_{ext} = \left\lceil \frac{P_{act} \cdot G}{N} \right\rceil},$while G is the number of guard subbands and “┌x┐” is a ceiling operatorthat provides the next higher integer for x. The number of inactivepilot subbands in the system is typically small if the number of guardsubbands is small. For example, the OFDM system described above may haveonly 10 inactive pilot subbands (i.e., P_(ext)=10) out of 512 pilotsubbands (i.e., P=512 ) if there are 80 guard subbands (i.e., G=80 ). Inthis case, the computation required for extrapolation does not greatlyincrease computational complexity. The computational complexity can alsobe reduced explicitly by restricting the extrapolation to use a subsetof the active pilots.

The extrapolation coefficients can be fixed and determined offline(i.e., pre-computed) based on a criterion such as least-squares, minimummean square error (MMSE), and so on. For least-squares extrapolation, acoefficient matrix C_(P) _(ext) _(×P) _(act) ^(ls) may be defined asfollows:C _(P) _(ext) _(×P) _(act) =W _(P) _(ext) _(×L)(W _(P) _(act) _(×L) ^(H)W _(P) _(act) _(×L))⁻¹ W _(P) _(act) _(×L) ^(H),   Eq. (13)where W_(P) _(ext) _(×L) is a P_(act)×L sub-matrix of W_(N×N). In apractical system, the matrix W_(P) _(act) _(×L) ^(H)W_(P) _(act) _(×L)may be “ill-conditioned”, which means that the computation of theinverse of this matrix may face numerical stability issues. In thiscase, a correction term may be used to get around the ill-conditioningproblem, and a modified least-squares extrapolation matrix${\underset{\_}{C}}_{P_{est} \times P_{act}}^{mls}$may be defined as follows:C _(P) _(ext) _(×P) _(act) ^(mls) =W _(P) _(ext) _(×L)(W _(P) _(act)_(×L) +δI)⁻¹ W _(P) _(act) _(×L) ^(H),   Eq. (14)where δ is a small correction factor.

For MMSE extrapolation, a coefficient matrix${\underset{\_}{C}}_{P_{est} \times P_{act}}^{mmse}$may be defined as follows: $\begin{matrix}{{{\underset{\_}{C}}_{P_{est} \times P_{act}}^{mmse} = {\eta\quad\gamma\quad{\underset{\_}{W}}_{P_{ext} \times L}{{\underset{\_}{W}}_{P_{act} \times L}^{H}\left( {{\gamma\quad{\underset{\_}{W}}_{P_{act} \times L}{\underset{\_}{W}}_{P_{act} \times L}^{H}} + \underset{\_}{I}} \right)}^{- 1}}},} & {{Eq}\quad(15)}\end{matrix}$where γ the signal-to-noise ratio (SNR) of the received pilot symbols;and

-   -   η is a factor used to derive an unbiased estimate.        In the absence of SNR information, γ may be considered as a        parameter that can be selected to optimize performance. The        factor η is a scalar quantity may also be used to optimize        performance. The vector        ${\hat{\underset{\_}{H}}}_{P_{est} \times 1}^{init}$        obtained with        ${\underset{\_}{C}}_{P_{est} \times P_{act}}^{mmse}$        is an MMSE estimate of the channel under the assumption that the        taps in the time-domain are uncorrelated and are of equal        energy. Equation (15) assumes that the autocovariance matrix of        the noise vector n_(P) _(act) _(×1) ^(p) for the P_(act) active        pilot subband is the identity matrix. Equation (15) may be        modified to account for this autocovariance matrix if it is        known by the receiver.

In yet another extrapolation scheme, the channel gain estimate for eachinactive pilot subband is set equal to zero, i.e., Ĥ(s_(i))=0 fors_(i)<s_(b) and s_(i)>s_(e). The extrapolation may also be performed inother manners, and this is within the scope of the invention. Forexample, functional extrapolation techniques such as linear andquadratic extrapolation may be used. Non-linear extrapolation techniquesmay also be used, which fall within the general framework of equation(12).

A pilot transmission scheme may not distribute the active pilot subbandsuniformly across the M usable subbands. In this case, interpolation mayalso be used to obtain channel gain estimates for uniformly spacedsubbands within the M usable subbands. The interpolation may beperformed in various manners, similar to that described above forextrapolation. In general, extrapolation and/or interpolation may beperformed as necessary based on the available received pilot symbols toobtain channel gain estimates for P subbands uniformly spaced across theN total subbands.

Tap Selection

For block 622 in FIG. 6, tap selection is performed on the vectorĥ_(P×1) ^(ls) to select good taps for the channel impulse responseestimate. The tap selection may be performed in various manners.

In one tap selection scheme, the channel impulse response estimateĥ_(P×1) ^(ls) is truncated to L values for the L taps of the wirelesschannel. The vector ĥ_(P×1) ^(ls) contains P elements, where P≧L. Forthis deterministic tap selection scheme, the first L elements of ĥ_(P×1)^(ls) are considered as good taps and retained, and the last P-Lelements are replaced with zeros. When L<P, the least squares channelimpulse response estimate with L taps can be obtained (without loss inperformance) by assuming a channel with P taps, performing a P-pointIFFT, and truncating the last P-L taps. This has some benefits incertain situations. For example, if L<P/2, then the least squareschannel impulse response estimate can be derived with the computationalbenefits of the FFT and not computing the last P/2 taps.

In another tap selection scheme, the elements of ĥ_(P×1) ^(ls) with lowenergy are replaced with zeros. These elements of ĥ_(P×1) ^(ls)correspond to taps with low energy, where the low energy is likely dueto noise rather than signal energy. A threshold is used to determinewhether a given element/tap has sufficient energy and should be retainedor should be zeroed out. This process is referred to as “thresholding”.

The threshold can be computed based on various factors and in variousmanners. The threshold can be a relative value (i.e., dependent on themeasured channel response) or an absolute value (i.e., not dependent onthe measured channel response). A relative threshold can be computedbased on the (e.g., total or average) energy of the channel impulseresponse estimate. The use of the relative threshold ensures that (1)the thresholding is not dependent on variations in the received energyand (2) the elements/taps that are present but with low signal energyare not zeroed out. An absolute threshold can be computed based on thenoise variance/noise floor at the receiver, the lowest energy expectedfor the received pilot symbols, and so on. The use of the absolutethreshold forces the elements of ĥ_(P×1) ^(ls) to meet some minimumvalue in order to be retained. The threshold can also be computed basedon a combination of factors used for relative and absolute thresholds.For example, the threshold can be computed based on the energy of thechannel impulse response estimate and further constrained to be equal toor greater than a predetermined minimum value.

The thresholding can be performed in various manners. In onethresholding scheme, the thresholding is performed after the truncationand may be expressed as: $\begin{matrix}{{\hat{h}(n)} = \left\{ {\begin{matrix}0 & {{{for}\quad{{\hat{h}(n)}}^{2}} < {\alpha \cdot {{{\hat{\underset{\_}{h}}}_{P \times 1}^{ls}}^{2}/L}}} \\{\hat{h}(n)} & {{otherwise}\quad}\end{matrix},{{{for}\quad n} = {{0\quad\ldots\quad L} - 1}}} \right.} & {{Eq}\quad(16)}\end{matrix}$where ĥ_(P×1) ^(ls)=[ĥ(0) ĥ(1) . . . ĥ(P−1)]^(T), where the last P-Lelements are replaced with zeros by the truncation;

-   -   |ĥ(n)|² is the energy of the n-th tap;    -   ∥ĥ_(P×1) ^(ls)∥² is the energy of the channel impulse response        estimate for the L taps; and    -   α·∥ĥ_(P×1) ^(ls)∥²/L is the threshold used to zero out low        energy elements/taps.        ∥x∥² is the norm of vector x and is equal to the sum of the        squares of all of the elements in the vector x.

In equation (16), the threshold is defined based on the average energyof the L taps. The coefficient α is selected based on a trade offbetween noise suppression and signal deletion. A higher value for αprovides more noise suppression but also increases the likelihood of alow signal energy element/tap being zeroed out. The coefficient α can bea value within a range of 0 to 1 (e.g., α=0.1). The threshold can alsobe defined based on the total energy (instead of the average energy) forthe channel impulse response estimate ĥ_(P×1) ^(ls). The threshold maybe fixed or adapted based on (1) the particular coding and modulationscheme or rate of the data stream being demodulated (2) a bit error rate(BER), packet error rate (PER), block error rate (BLER), or some othererror rate performance requirement, and/or (3) some other parameters andconsiderations.

In another thresholding scheme, the thresholding is performed on all Pelements of ĥ_(P×1) ^(ls) (i.e., without truncation) using a singlethreshold, similar to that shown in equation (16). In yet anotherthresholding scheme, the thresholding is performed on all P elements ofĥ_(P×1) ^(ls) using multiple thresholds. For example, a first thresholdmay be used for the first L elements of ĥ_(P×1) ^(ls), and a secondthreshold may be used for the last P-L elements of ĥ_(P×1) ^(ls). Thesecond threshold may be set lower than the first threshold. In yetanother thresholding scheme, the thresholding is performed on only thelast P-L elements of ĥ_(P×1) ^(ls) and not on the first L elements. Thethresholding may be performed in other manners, and this is within thescope of the invention.

Thresholding is well suited for a wireless channel that is “sparse”,such as a wireless channel in a macro-cellular broadcast system. Asparse wireless channel has much of the channel energy concentrated infew taps. Each tap corresponds to a resolvable signal path withdifferent time delay. A sparse channel includes few signal paths eventhough the delay spread (i.e., time difference) between these signalpaths may be large. The taps corresponding to weak or non-existingsignal paths can be zeroed out.

For block 518 in FIG. 5 and block 620 in FIG. 6, the channel impulseresponse estimate may be filtered in the time domain using a lowpassfilter such as a finite impulse response (FIR) filter, an infiniteimpulse response (IIR) filter, or some other type of filter. The lowpassfilter may be a causal filter (which performs filtering on past andcurrent samples) or a non-causal filter (which performs filtering onpast, current, and future samples obtained by buffering). Thecharacteristics (e.g., bandwidth) of the filter may be selected based onthe characteristics of the wireless channel. Time-domain filtering maybe performed separately for each tap of the channel impulse responseestimate across multiple OFDM symbols. The same or different filters maybe used for the taps of the channel impulse response estimate. Thecoefficients for each such filter may be fixed or may be adjustablebased on detected channel conditions. Performing the filtering in thetime domain has an advantage in that the pilot subbands can be staggeredin the frequency domain (i.e., different sets of pilot subbands may beused for different OFDM symbols). The staggering of pilot subbands isuseful when the channel has an excess delay spread (i.e., the channelimpulse response has a length greater than P taps). A channel impulseresponse estimate with more than P taps can be obtained with theadditional and different pilot subbands provided by staggering. Thefiltering may also be performed on the initial or final frequencyresponse estimates.

OFDM System

FIG. 7 shows a block diagram of an access point 700 and a terminal 750in a spectrally shaped OFDM system. On the downlink, at access point700, a transmit (TX) data processor 710 receives, formats, codes,interleaves, and modulates (i.e., symbol maps) traffic data and providesmodulation symbols (or simply, “data symbols”). An OFDM modulator 720receives and processes the data symbols and pilot symbols and provides astream of OFDM symbols. OFDM modulator 720 multiplexes data and pilotsymbols on the proper subbands, provides a signal value of zero for eachunused subband, and obtains a set of N transmit symbols for the Nsubbands for each OFDM symbol period. Each transmit symbol may be a datasymbol, a pilot symbol, or a signal value of zero. The pilot symbols maybe sent on active pilot subbands, as shown in FIG. 4. The pilot symbolsmay be sent continuously in each OFDM symbol period. Alternatively, thepilot symbols may be time division multiplexed (TDM) with the datasymbols on the same subband.

OFDM modulator 720 further transforms each set of N transmit symbols tothe time domain using an N-point IFFT to obtain a “transformed” symbolthat contains N time-domain chips. OFDM modulator 720 typically repeatsa portion of each transformed symbol to obtain a corresponding OFDMsymbol. The repeated portion is known as a cyclic prefix and is used tocombat delay spread in the wireless channel.

A transmitter unit (TMTR) 722 receives and converts the stream of OFDMsymbols into one or more analog signals and further conditions (e.g.,amplifies, filters, and frequency upconverts) the analog signals togenerate a downlink signal suitable for transmission over the wirelesschannel. The downlink signal is then transmitted via an antenna 724 tothe terminals.

At terminal 750, an antenna 752 receives the downlink signal andprovides a received signal to a receiver unit (RCVR) 754. Receiver unit754 conditions (e.g., filters, amplifies, and frequency downconverts)the received signal and digitizes the conditioned signal to obtainsamples. An OFDM demodulator 756 removes the cyclic prefix appended toeach OFDM symbol, transforms each received transformed symbol to thefrequency domain using an N-point FFT, obtains N received symbols forthe N subbands for each OFDM symbol period, and provides received pilotsymbols {{circumflex over (P)}_(dn)(s_(i))} to a processor 770 forchannel estimation. OFDM demodulator 756 further receives a frequencyresponse estimate Ĥ_(N×1,dn) for the downlink from processor 770,performs data demodulation on the received data symbols to obtain datasymbol estimates (which are estimates of the transmitted data symbols),and provides the data symbol estimates to an RX data processor 758. RXdata processor 758 demodulates (i.e., symbol demaps), deinterleaves, anddecodes the data symbol estimates to recover the transmitted trafficdata. The processing by OFDM demodulator 756 and RX data processor 758is complementary to the processing by OFDM modulator 720 and TX dataprocessor 710, respectively, at access point 700.

Processor 770 obtains the received pilot symbols for the active pilotsubbands and performs channel estimation as shown in FIGS. 5 and 6.Processor 770 performs extrapolation and/or interpolation as necessaryto obtain channel gain estimates for P_(dn) uniformly spaced subbands(where P_(dn) is the number of pilot subbands for the downlink), derivesa least square impulse response estimate ĥ_(P×1,dn) ^(ls) for thedownlink, performs tap selection for the P elements/taps of ĥ_(P×1,dn)^(ls), and derives the final frequency response estimate Ĥ_(N×1,dn)^(ls) for the N subbands for the downlink.

On the uplink, a TX data processor 782 processes traffic data andprovides data symbols. An OFDM modulator 784 receives and multiplexesthe data symbols with pilot symbols, performs OFDM modulation, andprovides a stream of OFDM symbols. The pilot symbols may be transmittedon P_(up) subbands that have been assigned to terminal 750 for pilottransmission, where the number of pilot subbands (P_(up)) for the uplinkmay be the same or different from the number of pilot subbands (P_(dn))for the downlink. The pilot symbols may also be multiplexed with thedata symbols using TDM. A transmitter unit 786 then receives andprocesses the stream of OFDM symbols to generate an uplink signal, whichis transmitted via an antenna 752 to the access point.

At access point 700, the uplink signal from terminal 150 is received byantenna 724 and processed by a receiver unit 742 to obtain samples. AnOFDM demodulator 744 then processes the samples and provides receivedpilot symbols {{circumflex over (P)}_(up)(s_(i))} and data symbolestimates for the uplink. An RX data processor 746 processes the datasymbol estimates to recover the traffic data transmitted by terminal750.

Processor 730 performs channel estimation for each active terminaltransmitting on the uplink as shown in FIGS. 5 and 6. Multiple terminalsmay transmit pilot concurrently on the uplink on their respectiveassigned sets of pilot subbands, where the pilot subband sets may beinterlaced. For each terminal m, processor 730 performs extrapolationand/or interpolation as needed for the terminal, obtains an initialfrequency response estimate${\hat{\underset{\_}{H}}}_{{P \times 1},{up}}^{{init},m}$for the uplink for the terminal, derives at least square channel impulseresponse estimate${\hat{\underset{\_}{h}}}_{{P \times 1},{up}}^{{ls},m}$for the terminal based on${\hat{\underset{\_}{H}}}_{{P \times 1},{up}}^{{init},m},$performs tap selection, and further obtains a final frequency responseestimate ${\hat{\underset{\_}{H}}}_{{N \times 1},{up}}^{{ls},m}$for the terminal. The frequency response estimate${\hat{\underset{\_}{H}}}_{{N \times 1},{up}}^{{ls},m}$for each terminal is provided to OFDM demodulator 744 and used for datademodulation for that terminal.

Processors 730 and 770 direct the operation at access point 700 andterminal 750, respectively. Memory units 732 and 772 store program codesand data used by processors 730 and 770, respectively. Processors 730and 770 also perform the computation described above to derive frequencyand impulse response estimates for the uplink and downlink,respectively.

For a multiple-access OFDM system (e.g., an orthogonal frequencydivision multiple-access (OFDMA) system), multiple terminals maytransmit concurrently on the uplink. For such a system, the pilotsubbands may be shared among different terminals. The channel estimationtechniques may be used in cases where the pilot subbands for eachterminal span the entire operating band (possibly except for the bandedges). Such a pilot subband structure would be desirable to obtainfrequency diversity for each terminal.

The channel estimation techniques described herein may be implemented byvarious means. For example, these techniques may be implemented inhardware, software, or a combination thereof. For a hardwareimplementation, the processing units used for channel estimation may beimplemented within one or more application specific integrated circuits(ASICs), digital signal processors (DSPs), digital signal processingdevices (DSPDs), programmable logic devices (PLDs), field programmablegate arrays (FPGAs), processors, controllers, micro-controllers,microprocessors, other electronic units designed to perform thefunctions described herein, or a combination thereof.

For a software implementation, the channel estimation techniques may beimplemented with modules (e.g., procedures, functions, and so on) thatperform the functions described herein. The software codes may be storedin a memory unit (e.g., memory units 732 and 772 in FIG. 7) and executedby a processor (e.g., processors 730 and 770). The memory unit may beimplemented within the processor or external to the processor, in whichcase it can be communicatively coupled to the processor via variousmeans as is known in the art.

Headings are included herein for reference and to aid in locatingcertain sections. These headings are not intended to limit the scope ofthe concepts described therein under, and these concepts may haveapplicability in other sections throughout the entire specification.

The previous description of the disclosed embodiments is provided toenable any person skilled in the art to make or use the presentinvention. Various modifications to these embodiments will be readilyapparent to those skilled in the art, and the generic principles definedherein may be applied to other embodiments without departing from thespirit or scope of the invention. Thus, the present invention is notintended to be limited to the embodiments shown herein but is to beaccorded the widest scope consistent with the principles and novelfeatures disclosed herein.

1. A method of estimating a frequency response of a wireless channel ina wireless communication system, comprising: obtaining an initialfrequency response estimate for a first set of P uniformly spacedsubbands based on channel gain estimates for a second set ofnon-uniformly spaced subbands, where P is an integer greater than oneand is a power of two, and wherein the first set includes at least onesubband not included in the second set; deriving a time-domain channelimpulse response estimate for the wireless channel based on the initialfrequency response estimate; and deriving a final frequency responseestimate for the wireless channel based on the channel impulse responseestimate.
 2. The method of claim 1, further comprising: deriving thechannel gain estimates for the second set of subbands based on pilotsymbols received on the subbands in the second set.
 3. The method ofclaim 1, wherein the deriving a time-domain channel impulse responseestimate includes performing a P-point inverse fast Fourier transform(IFFT) on the initial frequency response estimate to obtain the channelimpulse response estimate.
 4. The method of claim 1, wherein thederiving a final frequency response estimate includes zero padding thechannel impulse response estimate to length S, where S is an integergreater than or equal to P and is a power of two, and performing anS-point fast Fourier transform (FFT) on the zero-padded channel impulseresponse estimate to obtain the final frequency response estimate. 5.The method of claim 4, wherein S is equal to total number of subbands inthe system.
 6. The method of claim 1, wherein the first set includes Psubbands uniformly spaced among N total subbands, wherein the second setincludes subbands in the first set that are among M usable subbands, andwherein the M usable subbands are a subset of the N total subbands. 7.The method of claim 1, further comprising: performing extrapolationbased on the received pilot symbols to obtain at least one channel gainestimate for the at least one subband not included in the second set,and wherein the initial frequency response estimate includes the atleast one channel gain estimate.
 8. The method of claim 1, furthercomprising: performing interpolation based on the received pilot symbolsto obtain at least one channel gain estimate for the at least onesubband not included in the second set, and wherein the initialfrequency response estimate includes the at least one channel gainestimate.
 9. The method of claim 1, further comprising: obtaining achannel gain estimate for each of the at least one subband based on achannel gain estimate for a nearest subband.
 19. The method of claim 1,further comprising: obtaining a channel gain estimate for each of the atleast one subband based on a weighted sum of the channel gain estimatesfor the second set of subbands.
 11. The method of claim 1, wherein thechannel impulse response estimate includes P taps, and wherein selectedones of the P taps are set to zero.
 12. The method of claim 1, furthercomprising: filtering the channel impulse response estimate, and whereinthe final frequency response estimate is derived based on the filteredchannel impulse response estimate.
 13. The method of claim 1, furthercomprising: filtering the final frequency response estimate to obtain ahigher quality frequency response estimate for the wireless channel. 14.The method of claim 1, wherein the wireless communication system is anorthogonal frequency division multiplexing (OFDM) communication system.15. An apparatus in a wireless communication system, comprising: ademodulator operative to provide received symbols; and a processoroperative to obtain an initial frequency response estimate for a firstset of P uniformly spaced subbands based on channel gain estimates for asecond set of non-uniformly spaced subbands derived from the receivedsymbols, where P is an integer greater than one and is a power of two,wherein the first set includes at least one subband not included in thesecond set, derive a time-domain channel impulse response estimate forthe wireless channel based on the initial frequency response estimate,and derive a final frequency response estimate for the wireless channelbased on the channel impulse response estimate.
 16. The apparatus ofclaim 15, wherein the processor is further operative to performextrapolation or interpolation based on the received pilot symbols toobtain at least one channel gain estimate for the at least one subbandnot included in the second set, and wherein the initial frequencyresponse estimate includes the at least one channel gain estimate. 17.The apparatus of claim 15, wherein the processor is further operative toset selected ones of P taps for the channel impulse response estimate tozero.
 18. The apparatus of claim 15, wherein the processor is furtheroperative to filter the channel impulse response estimate, and whereinthe final frequency response estimate is derived based on the filteredchannel impulse response estimate.
 19. An apparatus in a wirelesscommunication system, comprising: means for obtaining an initialfrequency response estimate for a first set of P uniformly spacedsubbands based on channel gain estimates for a second set ofnon-uniformly spaced subbands, where P is an integer greater than oneand is a power of two, and wherein the first set includes at least onesubband not included in the second set; means for deriving a time-domainchannel impulse response estimate for the wireless channel based on theinitial frequency response estimate; and means for deriving a finalfrequency response estimate for the wireless channel based on thechannel impulse response estimate.
 20. The apparatus of claim 19,further comprising: means for performing extrapolation based on thereceived pilot symbols to obtain at least one channel gain estimate forthe at least one subband not included in the second set, and wherein theinitial frequency response estimate includes the at least one channelgain estimate.
 21. The apparatus of claim 19, further comprising: meansfor setting selected ones of P taps for the channel impulse responseestimate to zero.
 22. The apparatus of claim 19, further comprising:means for filtering the channel impulse response estimate, and whereinthe final frequency response estimate is derived based on the filteredchannel impulse response estimate.
 23. A method of estimating afrequency response of a wireless channel in a wireless communicationsystem, comprising: obtaining an initial frequency response estimate fora set of P subbands, where P is an integer greater than one; deriving atime-domain channel impulse response estimate with P taps for thewireless channel based on the initial frequency response estimate;setting selected ones of the P taps of the channel impulse responseestimate to zero; and deriving a final frequency response estimate forthe wireless channel based on the channel impulse response estimate withselected ones of the P taps set to zero.
 24. The method of claim 23,wherein last P-L taps of the channel impulse response estimate are setto zero, where L is an integer greater than one and less than P.
 25. Themethod of claim 23, wherein last P-L taps of the channel impulseresponse estimate are not derived from the initial frequency responseestimate.
 26. The method of claim 24, wherein L is equal to an expecteddelay spread for the system.
 27. The method of claim 23, furthercomprising: determining energy of each of the P taps; and setting eachof the P taps to zero if the energy of the tap is less than a threshold.28. The method of claim 27, wherein the threshold is derived based ontotal energy of the P taps for the channel impulse response estimate.29. The method of claim 27, wherein the threshold is derived based on acoding and modulation scheme selected for use.
 30. The method of claim27, wherein the threshold is derived based on error rate performancerequirement.
 31. The method of claim 23, further comprising: determiningenergy of each of the P taps; setting each of first L taps to zero ifthe energy of the tap is less than a first threshold, where L is aninteger greater than one and less than P; and setting each of last P-Ltaps to zero if the energy of the tap is less than a second thresholdthat is lower than the first threshold.
 32. A method of estimating afrequency response of a wireless channel in a wireless communicationsystem, comprising: obtaining an initial frequency response estimate fora set of P subbands, where P is an integer greater than one; deriving atime-domain channel impulse response estimate for the wireless channelbased on the initial frequency response estimate; filtering the channelimpulse response estimate over a plurality of symbol periods; andderiving a final frequency response estimate for the wireless channelbased on the filtered channel impulse response estimate.
 33. The methodof claim 32, wherein the channel impulse response estimate includes Ptaps, and wherein the filtering is performed separately for each of Ltaps, where L is an integer greater than one and less than P.
 34. Themethod of claim 32, wherein the filtering is based on a finite impulseresponse (FIR) filter or an infinite impulse response (IIR) filter. 35.The method of claim 32, wherein the filtering is based on a causalfilter.
 36. The method of claim 32, wherein the filtering is based on anon-causal filter.
 37. A method of estimating a frequency response of awireless channel in an orthogonal frequency division multiplexing (OFDM)communication system, the method comprising: obtaining an initialfrequency response estimate for a first set of P uniformly spacedsubbands based on channel gain estimates derived from pilot symbolsreceived on a second set of non-uniformly spaced subbands, where P is aninteger greater than one and is a power of two, and wherein the firstset includes at least one subband not included in the second set;performing a P-point inverse fast Fourier transform (IFFT) on theinitial frequency response estimate to obtain a time-domain channelimpulse response estimate; zero padding the channel impulse responseestimate to length N, where N is an integer greater than P and is apower of two; and performing an N-point fast Fourier transform (FFT) onthe zero-padded channel impulse response estimate to obtain a finalfrequency response estimate for the wireless channel.
 38. The method ofclaim 37, further comprising: performing extrapolation based on thereceived pilot symbols to obtain at least one channel gain estimate forthe at least one subband not included in the second set, and wherein theinitial frequency response estimate includes the at least one channelgain estimate.
 39. The method of claim 37, further comprising: settingselected ones of P taps for the channel impulse response estimate tozero.
 40. A processor readable media for storing instructions operableto: derive an initial frequency response estimate for a first set of Puniformly spaced subbands in an orthogonal frequency divisionmultiplexing (OFDM) communication system based on channel gain estimatesfor a second set of non-uniformly spaced subbands, where P is an integergreater than one and is a power of two, and wherein the first setincludes at least one subband not included in the second set; perform aP-point inverse fast Fourier transform (IFFT) on the initial frequencyresponse estimate to obtain a time-domain channel impulse responseestimate; zero pad the channel impulse response estimate to length N,where N is an integer greater than P and is a power of two; and performan N-point fast Fourier transform (FFT) on the zero-padded channelimpulse response estimate to obtain a final frequency response estimatefor a wireless channel in the system.